annulus_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of an annulus centered at the origin.
The interior of the disk is defined by
r1^2 <= x^2 + y^2 <= r2^2
The integrands are all of the form
f(x,y) = x^e1 * y^e2
where the exponents are nonnegative integers.
If any exponent is an odd integer, the integral will be zero.
Thus, the "interesting" results occur when all exponents are even.
The computer code and data files described and made available on this web page are distributed under the MIT license
annulus_integrals is available in a MATLAB version.
annulus_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the interior of an annulus centered at the origin.
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tetrahedron_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
triangle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.
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